Kulenovic; Mustafa R. S. University of Rhode Island, Kingston, Rhode Island, USA
Ladas; Gerasimos University of Rhode Island, Kingston, Rhode Island, USA

Dynamics of Second Order Rational Difference Equations:
With Open Problems and Conjectures

ISBN: 1-58488-275-1 No. of Pages: 240
Publication date: 7/27/2001

Description

This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications.

Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research projects or Ph.D. theses. Clear, simple, and direct exposition combined with thoughtful uniformity in the presentation make Dynamics of Second Order Rational Difference Equations valuable as an advanced undergraduate or a graduate-level text, a reference for researchers, and as a supplement to every textbook on difference equations at all levels of instruction.

Rocha-Chavez; Reynaldo ESFM-IFN, Mexico City, Mexico
Shapiro; Michael ESFM-IFN, Mexico City, Mexico
Sommen; Frank University of Ghent, Gent, Belgium

Integral Theorems for Functions and Differential Forms in C(m)

ISBN: 1-58488-246-8 No. of Pages: 232
Publication date: 8/16/2001

Description

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories.

The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain.

In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.

Lee; Dong Hoon Case Western Reserve University, Cleveland, Ohio USA

The Structure of Complex Lie Groups

ISBN: 1-58488-261-1 No. of Pages: 224
Publication date: 9/21/2001

Description

Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.

The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.

The differences between complex algebraic groups and complex Lie groups are sometimes subtle and it can be difficult to know which aspects of algebraic group theory apply and which must be modified. The Structure of Complex Lie Groups helps clarify those distinctions. Clearly written and well organized, this unique work presents material not found in other books on Lie groups and serves as an outstanding complement to them.

Velarde; Manuel G Instituto PluriDisciplinar, Madrid, Spain
Nepomnyashchy; Alexander A Technion, Haifa, Israel
Colinet; Pierre Universite Libre de Bruxelles, Bruxelles, Belgium

Interfacial Phenomena and Convection

ISBN: 1-58488-256-5
Publication date: 10/15/2001
Description

Interfacial phenomena driven by heat or mass transfer are widespread in science and various branches of engineering. Research in this area has become quite active in recent years, attributable in part, at least, to the entry of physicists and their sophisticated experimental techniques into the field. Until now, however, the field has lacked a readable account of the recent developments.

Interfacial Phenomena and Convection remedies this problem by furnishing a self-contained monograph that examines a rich variety of phenomena in which interfaces pay a crucial role. From a unified perspective that embraces physical chemistry, fluid mechanics, and applied mathematics, the authors study recent developments related to the Marangoni effect, including patterned convection and instabilities, oscillatory/wavy phenomena, and turbulent phenomena. They examine Board layers subjected to transverse and longitudinal thermal gradients and phenomena involving surface tension gradients as the driving forces, including falling films, drops, and liquid bridges.

It is only in the past two or three decades that researchers have performed suitable, clear-cut experiments involving interfacial phenomena, and the stage is now set for a virtual explosion of the field. Interfacial Phenomena and Convection will bring you quickly up to date on the advances realized and prepare you to both use the results and to make further advances.

Raftery; Adrian E. University of Washington, Seattle, Washington, USA
Tanner; Martin A. Northwestern University, Evanston, Illinois, USA
Wells; Martin T. Cornell University, Ithaca, New York, USA

Statistics in the 21st Century

ISBN: 1-58488-272-7 No. of Pages: 512
Publication date: 7/13/2001
Description

Exactly what is the state of the art in statistics as we move forward into the 21st century? What promises, what trends does its future hold? Through the reflections of 70 of the world's leading statistical methodologists, researchers, theorists, and practitioners, Statistics in the 21st Century answers those questions.

Originally published in the Journal of the American Statistical Association, this collection of vignettes examines our statistical past, comments on our present, and speculates on our future. Although the coverage is broad and the topics diverse, it reveals the essential intellectual unity of the field as we see the same themes recurring in different contexts. We see how the development of statistics has been driven by the unprecedented and still growing range of applications, by the explosion in computer technology, and by the new types of data that continue to emerge and advance the discipline.

Organized around major areas of application and leading up to vignettes on theory and methods, Statistics in the 21st Century forms a landmark record of the progress and perceived future of the discipline. No student, researcher, or practitioner of statistics should miss this extraordinary opportunity to view the past, present, and future world of statistics through the eyes of its foremost thinkers.